Geometric Properties of Some Familiar Diffusions in $\mathbb{R}^n$
Borell, Christer
Ann. Probab., Tome 21 (1993) no. 4, p. 482-489 / Harvested from Project Euclid
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Consider a convex domain $B$ in $\mathbb{R}^n$ and denote by $p(t, x, y)$ the transition probability density of Brownian motion in $B$ killed at the boundary of $B$. The main result in this paper, in particular, shows that the function $s \ln s^np(s^2, x, y), (s, x, y) \in \mathbb{R}_+ \times B^2$, is concave.
Publié le : 1993-01-14
Classification:  Concave,  transition probability density of killed Brownian motion,  Brunn-Minkowski inequality,  60J60,  60J65,  58G11 
@article{1176989412,
     author = {Borell, Christer},
     title = {Geometric Properties of Some Familiar Diffusions in $\mathbb{R}^n$},
     journal = {Ann. Probab.},
     volume = {21},
     number = {4},
     year = {1993},
     pages = { 482-489},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176989412}
}

Borell, Christer. Geometric Properties of Some Familiar Diffusions in $\mathbb{R}^n$. Ann. Probab., Tome 21 (1993) no. 4, pp.  482-489. http://gdmltest.u-ga.fr/item/1176989412/